Question

if radius of earth become half of its present value then the duration the day become ​

Answer 1

Answer:

the duration of day will decrease to ¼ the original value

Explanation:

The basic concept to solve the above question is to conserve the angular momentum before and after the shrinking of Earth:-

i1=initial moment of inertia

i2=final moment of inertia

w1=initial angular velocity

w2=final angular velocity

$i1w1 = i2w2 \: \: \: \: ...........(1)$

the moment of inertia of a solid sphere=$\frac{2}{5} \times mass \: of \: sphere \times {radius \: of \: sphere}^{2}$

as the radius of the earth becomes half, the moment of inertia will become ¼the initial value.

so, according to equation (1) :-

w2=4 w1........(2) (because i2=¼ i1)

initially duration of day was= angle rotated by earth÷ angular velocity

of earth about its axis(w1)

=24hours...............(3)

according to equation (2)and(3) :-

as the angular velocity is increased 4 times and the angle to be rotated is still 2π.

So, the duration of a day will be decrease by 4 times and will become 6 hours.

plZ MaRK as BrAinLIesT.

follow If that helped.

Answer 2

Answer:

If radius of earth become half of its present value then the duration the day become ​6 hours.

Explanation:

Let R be the radius of the earth.

We know that,

Angular momentum(L)=Iω=2/5MR²ω

Considering mass and velocity to be constant,

L₁=2/5MR²ω₁

When the radius of earth is divided by two,

L₂=2/5M(R/2)²ω₂

On calculating we get,

ω₂=4ω₁

The relation between T and ω is given by,

T₂/T₁=ω₁/ω₂

∴T₂=T₁/4

We know that, T₁=24

∴T₂=24/4=6hours

Therefore, if radius of earth become half of its present value then the duration the day become ​6 hours.